A Private Party sale would net you more money but as you noted, take more time. Mustang pricing varies by region and here in the Southeast, 2011/12 Mustang prices are in the dirt, Base GT's are less than 14-k, A couple Cali Packages are 18,5. Pricing around Houston looks to be a little better.
You know your financial situation better than us, but If you can deal with the tire kickers, joy riders and Craigslist Killers, advertise it for sale for 5-6 weeks, If it doesn't sell, I'll agree with TJ, if the dealer is offering a decent price, let em have it.
If you buy another car from the dealer, aka trade yours in, remember you'll get tax savings on your trade in as well since you've already been taxed on the one you're trading. Here in Texas tax on cars is 6.25% so trading in for 18500 would next you $1,156 in tax savings essentially getting you 19656 for your trade.